Decoding low density parity codes

Abstract

The present invention includes a technique for updating messages that originate at the constraint nodes of bi-partite graphs in Low Density Parity Check codes. The technique computes only two outgoing magnitudes at each constraint node and exhibits no measurable performance loss as compared to exact belief propagation which computes a unique magnitude for each departing edge from a given constraint node. The technique eliminates the need for memory based table look-up in the constraint node processing and has been implemented, in one embodiment, using only shift, add, and comparison operations.

Description

[0001]This application claims the benefit of U.S. Provisional Application No. 60 / 510,183, “Decoding Low Density Parity Codes” filed on Oct. 10, 2003, which is incorporated herein by reference in its entirety.[0002]This invention was made with Government support of Grant No. N00014-01-C-0016, awarded by the Office of Naval Research. The Government has certain rights in this invention.BACKGROUND OF THE INVENTION[0003]1. Field of the Invention[0004]The present invention is directed to technology relevant to decoding Low Density Parity codes.[0005]2. Description of the Related Art[0006]Communication technology has become more important and has received greater attention as more people communicate via computer networks, telephone networks and various wireless networks. The goal is to communicate data in a reliable and efficient manner. However, data being communicated can be corrupted. For example, wireless data (e.g. digital or analog, voice or non-voice) is subject to noise.[0007]There...

AI Technical Summary

Benefits of technology

[0014]The present invention, roughly described, relates to technology for decoding LDPC codes. In one embodiment, the system computes only two unique magnitudes per constraint node, rather than the number dc of messages associated with a constraint node and / or uses combinational logic rather than table look-up to approximate the non-linear portion of the constraint update. A reduced complexity decoding algorithm that suffers little or no performance loss has been developed and is justified both theoretically and experimentally. Finite word lengths have been carefully considered and 6 to 7 bits of precision have been shown to be adequate for a highly complex (a length of 10,000 dmax=20 irregular LDPC) code to achieve an error floor that is code rather than implementation limited. The technique eliminates the need for memory based table look-up in the constraint node processing and has been implemented, in one embodiment, using only shift, add, and comparison operations.

Problems solved by technology

However, data being communicated can be corrupted.

For example, wireless data (e.g. digital or analog, voice or non-voice) is subject to noise.

First, there is ARQ, which includes re-transmitting data if there is a problem.

Second, there is Forward Error Correction (FEC), which includes using codes with the data to detect and, possibly, correct, corrupt data.

The problem being solved with FEC is how much redundancy to add in an intelligent manner to make sure that the data arrives correctly.

Long codes do a better job insuring correctness, but are more complex and harder to work with.

However, these codes were too short for the sphere packing bound to approach Shannon capacity, and the computational resources for longer random codes were decades away from being broadly accessible.

However, this form still posses significant processing challenges as it employs a non-linear function that must be represented with a large dynamic range for optimal performance.

Even Full-BP algorithms suffer performance degradation as compared to the optimum Maximum Likelihood (ML) decoder for a given code.

This is due to the fact that bipartite graphs representing finite-length codes without singly connected nodes are inevitably non-tree-like.

Cycles in bipartite graphs compromise the optimality of belief propagation decoders.

Establishing the true ML performance of LDPC codes with length beyond a few hundred bits is generally viewed as an intractable problem.

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